Aiming at the problem that the soft sensing precision of key variables deteriorates when unmodeled dynamics and uncertain disturbances exist in the complex industrial process

an on-line soft sensor based on stable Hammerstein model (H model) was presented. H model was composed of wavelet neural network with time-varying stable learning algorithm as nonlinear gain and ARX model with RLS (recursive least square) algorithm as linear part. The boundedness of identification error for H model was proved according to the Input-to-State Stability theory. Wavelet neural network could represent strong nonlinearity of the process

and the stable learning algorithm could restrain the influences of unmodeled dynamics and uncertain disturbances and improve prediction precision and self-adaptability. Simulations based on a nonlinear system and the wastewater treatment process showed that the soft sensing method presented in this paper possessed high prediction precision.